Gylfi Sigurdsson did reduce the deficit late on for the visitors but Saints managed to hang on and claim an important three points in their fight against the drop.
The hosts looked the more likely in the first half as both Nathan Redmond and Danny Ings came close, with both denied by the woodwork.
It took a moment of brilliance from Ward-Prowse to break the deadlock five minutes after the restart as he smashed a superb 20-yard effort into the top corner, leaving Jordan Pickford no chance in the Everton goal.
Southampton enjoyed more than a slice of luck for their second as Digne scored a bizarre own goal from 25 yards with a toe-poke. That goal may have been fortunate for Saints but they were good value for their lead regardless.
However, they had to hold on at the end after Sigurdsson's late effort into the bottom corner.
Everton committed men forward in search of an equaliser but Saints held on as they continued their revival under manager Ralph Hasenhuttl, with 13 points from a possible 24 since the Austrian took charge.